{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 可视化三维样本数据点的PCA过程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from mpl_toolkits import mplot3d\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 在三维空间随机生成100个样本点\n",
    "np.random.seed(8888)\n",
    "X_random = np.random.random(size=(100, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X_random[:,0], X_random[:,1], X_random[:,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### demean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "def demean(X):\n",
    "    return X - np.mean(X, axis=0)\n",
    "\n",
    "X = demean(X_demean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X[:,0], X[:,1], X[:,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(w, X):\n",
    "    return np.sum((X.dot(w)**2)) / len(X)\n",
    "\n",
    "def df(w, X):\n",
    "    return X.T.dot(X.dot(w)) * 2. / len(X)\n",
    "\n",
    "def direction(w):\n",
    "    return w / np.linalg.norm(w)\n",
    "\n",
    "def first_component(X, initial_w, eta, n_iters = 1e4, epsilon=1e-8):\n",
    "    \n",
    "    w = direction(initial_w) \n",
    "    cur_iter = 0\n",
    "\n",
    "    while cur_iter < n_iters:\n",
    "        gradient = df(w, X)\n",
    "        last_w = w\n",
    "        w = w + eta * gradient\n",
    "        w = direction(w) \n",
    "        if(abs(f(w, X) - f(last_w, X)) < epsilon):\n",
    "            break\n",
    "            \n",
    "        cur_iter += 1\n",
    "\n",
    "    return w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.79844556,  0.17774691, -0.57523102])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_w = np.random.random(X.shape[1])\n",
    "eta = 0.01\n",
    "w1 = first_component(X, initial_w, eta) \n",
    "w1 # 求出第一主成分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将原来的所有样本点X去除在第一主成分上的分量，得到X2\n",
    "X2 = np.empty(X_demean.shape)\n",
    "for i in range(len(X)):\n",
    "    X2[i] = X[i] - X[i].dot(w1) * w1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制X2，此时，X2的所有样本点分布在一个平面上\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X2[:,0], X2[:,1], X2[:,2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.55126946, -0.59994224,  0.5798028 ])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w2 = first_component(X2, initial_w, eta)\n",
    "w2 # 求出第二主成分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将X2去除在第二主成分上的分量，得到X3\n",
    "X3 = np.empty(X2.shape)\n",
    "for i in range(len(X)):\n",
    "    X3[i] = X2[i] - X2[i].dot(w2) * w2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制X3，此时，X3的所有样本点分布在一条直线上\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.scatter3D(X3[:,0], X3[:,1], X3[:,2])\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
